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Algebra Terms
| Question | Answer |
|---|---|
| Absolute Value | makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written |x|. We write |–6| |
| Real Numbers | The numbers we use to measure real-world quantities, such as length, temperature, or volume, are called real numbers. All the rational and irrational numbers make up the set of real numbers. The number line is a model of the set of real numbers. |
| Rational Number | A number that can be expressed as the quotient of two integers. Fractions, mixed numbers, decimals and integers are all rational numbers, because they may be expressed as a quotient of two integers. Ex: 3 1/4 |
| Irrational Number | Some numbers cannot be written as a quotient of two integers, and these are called irrational numbers. |
| Variable | A letter that stands for a number in a mathematical expression is called a 'var'iable, because its value can vary. In the expression 4n + 7, n is a variable |
| Expression | A mathematical phrase made up of variables and/or numbers and operations is called an expression. Ex: 2ab + 3ab - a |
| Terms | in an expression, the terms are the elements separated by the plus or minus signs. In the expression 2ab + 3ab - a, the terms are 2ab, 3 ab, and a |
| Coefficient | A number that appears before a letter in a term. For example in the term 2ab, 2 is the coefficient. |
| Constant | A term that has only one number and no variables is called a constant, because its value doesn't vary. In the expression 2ab + 3b + 6, the number 6 is a constant |
| Algebraic Expressions | An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It's only a phrase, not the whole sentence, so it doesn't include an equal sign. |
| the sum of three times a number and eight | 3x + 8 |
| The words ""the sum of"" tell us we need a plus sign because we're going to add three times a number to eight. The words ""three times"" tell us the first term is a number multiplied by three. | |
| In this expression, we don't need a multiplication sign or parenthesis. Phrases like ""a number"" or ""the number"" tell us our expression has an unknown quantity, called a variable. In algebra, we use letters to represent variables. | |
| the product of a number and the same number less 3 | x(x – 3) |
| The words ""the product of"" tell us we're going to multiply a number times the number less 3. In this case, we'll use parentheses to represent the multiplication. The words ""less 3"" tell us to subtract three from the unknown number. " | |
| a number divided by the same number less five | x/x-5 |
| The words ""divided by"" tell us we're going to divide a number by the difference of the number and 5. In this case, we'll use a fraction to represent the division. The words ""less 5"" tell us we need a minus sign because we're going to subtract five." | |
| A number n times 3 is equal to 120. | A number n times 3 is equal to 120. |
| This is an easy one. The word ""times"" tells you that you must multiply the variable n by 3, and that the result is equal to 120. Here's how to write this equation: " | |
| Commutative property of Addition | a+b = b+a |
| Commutative property of Multiplication | ab = ba |
| Associative Property of Addition | (a+b) + c = a + (b+c) |
| Associative Property of Multiplication | (ab)c = a(bc) |
| Distributive Property | a(b+c) = ab + ac |
| Density Property | Between any two real numbers, there is always another real number. |
| Identity Property of Addition | a + 0 = a |
| Identity Property of Multiplication | a * 1 = a |
| ≥ | greater than or equal to |
| ≤ | less than or equal to |
| > | greater than |
| < | less than |
| Solving addition and subtraction equations | To solve an equation means to find a value for the variable that makes the equation true. Whatever you do to one side of the equation, you must also do to the other side. (Balance the scale) |
| Solving multiplication equations | To solve a multiplication equation, use the inverse operation of division. Divide both sides by the same non-zero number. |
| Solving division equations | To solve a division equation, use the inverse operation of multiplication. Multiply both sides by the same number. |
| Inequalities | A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥. |
| Exponent | The number (written in superscript) used to express how many times a base is multiplied by itself |
| Base | The number directly preceeding an exponent |
| polynomial | is a series of one or more terms that are added or subtracted, such as 3x + 2y - 4 |
| To change from percent to decimal | you move the decimal point two places to the right |
| 9 + 10 = | You thought I was gonna do it, didn't you? |
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